Post-yield Fracture Mechanics Research Articles

Post-yield fracture correlations to morphological and micromechanical response of poly(ε-caprolactone)-based biocomposites

The present work investigates the effect of jack wood flour (JWF) content on the fracture toughness, tensile, impact, and morphological behavior of the prepared green biocomposites. From 0 to 35 wt% (volume fraction ( Φf) = 0–0.34) of JWF was incorporated as a reinforcing biodegradable filler into poly(ε-caprolactone) (PCL) matrix by melt compounding in a twin screw extruder. The tensile modulus increases by 80.48% at the highest Φf= 0.34, though marginal increment (13.71%) in the yield strength was registered. A sharp reduction in notched Izod impact strength (85%) was observed with increasing JWF content. The fracture toughness of the prepared biocomposites based on post-yield fracture mechanics concept was investigated by essential work of fracture (EWF) methodology. Incorporation of JWF into PCL matrix diminishes the EWF ( we), while increasing the non-essential work of fracture ( βwp). In the biocomposites, principally two mechanisms governed the fracture deformation. Large JWF particles act as stress concentration points and favor the crack initiation, while the smaller particles favor fibrillation which arrests the crack propagation enhancing the parameter βwpat lower concentration of JWF. Freeze-fractured surfaces show a degree of phase adhesion at lower Φfof JWF. The phase adhesion parameter obtained from micromechanical analysis of tensile properties suggesting the mechanical interlocking and interaction between PCL and JWF.

Post-yield crack toughness behavior of polyamide-6/polypropylene grafted maleic anhydride/nanoclay ternary nanocomposites

The fracture properties of melt-mixed polyamide-6 (PA-6)/polypropylene grafted maleic anhydride (PP-g-MA)/nanoclay ternary nanocomposites were investigated following essential work of fracture (EWF) approach based on post-yield fracture mechanics principles. Fourier transform infrared (FTIR) spectroscopy studies revealed distinct interactions between optimized impact-modified PA-6 based blend matrix and nanoclay whereas the incorporation of nanoclay leading to enhanced lighter phase-contrast atomic force microscope (AFM) images have indicated enhanced hard-phase fractions. FTIR revealed tripartite interactions between amide functionality, maleic anhydride moiety and hydroxyl group of the three constituents of the nanocomposite. The validity of essential work of fracture (EWF) concept to these ternary nanocomposites has been demonstrated via self-similarity and Hill’s analysis. The EWF (we) showed an increase by ∼35% with the incorporation of 2wt.% of nanoclay followed by a continuous reduction up to ∼67% in 6wt.% of nanoclay loaded composite whereas non-EWF (βwp) increased almost consistently with the maximum up to ∼264% in the entire composition range. Thus linear increase in the resistance to crack propagation is attributed to nanoclay induced enhanced micro-fibrillation accompanied with the generation of fracture surface as revealed from scanning electron microscopy studies.

Kinetic and structural interpretations of post-yield crack resistance behavior of polyamide-6/polyolefin-g-maleic anhydride blends

Binary blends of polyamide-6 (PA-6)/polypropylene-grafted-maleic anhydride (PP-g-MA) and PA-6/low density polyethylene-grafted-maleic anhydride (LDPE-g-MA) were prepared with varied concentration (0–30 wt%) of maleic anhydride-grafted polyolefinic (PP) moiety as the impact modifier. The microstructural attributes and thermal properties of the blends were characterized by WAXD, FTIR, SEM, DSC, and TGA. The WAXD/DSC studies have revealed that the crystallinity of the blends decreased with the increase in the PP modifier whereas the onset of degradation temperature remained nearly unaffected. Comparative assessment of the crack toughness behavior of the blends has been carried out following the essential work of fracture (EWF) approach based on post-yield fracture mechanics (PYFM) concept. The kinetics of crack propagation of the blends has been discussed in the realms of structural and compositional parameters. An enhancement in the toughness (resistance to stable crack propagation) as indicated by a maximum in the non-EWF (βw p) values have been observed at 10 and 20 wt% followed by a sharp and consistent drop in the composition regime of 10–20 and 20–30 wt% of PP-g-MA and LDPE-g-MA, respectively; conceptually implying possible ductile-to-semiductile transitions in the blend systems. The equivalence of PYFM–EPFM fracture parameters have been discussed following inequality criterion. Fractured surface morphology investigations revealed that the failure mode of the blends undergo a systematic transition from matrix-controlled homogeneous flow/deformation in the PP/polyamide phase to blend composition-dependent changes in the modes and extent of fibrillation via cavitation and shear-banding mechanisms.

Ductile-to-brittle transition in cenosphere-filled polypropylene composites

Cenosphere-filled polypropylene (PP) composites were fabricated and characterized for their structural/morphological and fracture mechanical behaviour. The fracture properties were studied following the essential work of fracture (EWF) approach based on post-yield fracture mechanics (PYFM) concept. The structural attributes and its consequent effects on the dynamic mechanical properties were characterized by wide angle X-ray diffraction (WAXD), hot-stage polarized light optical microscopy (PLOM) and dynamic mechanical analysis (DMA). The WAXD studies have revealed a decrease in crystallinity of the composites with increase in cenosphere content. PLOM studies reveals a threefold reduction in the diameter of the spherulite in case of composite with 10 wt% of cenosphere compared to that of PP followed by an increase of ~50% in the composite with 20 wt% of cenosphere compared to that of the composite with 10 wt% cenosphere. DMA revealed an enhancement in the energy dissipation ability of the composite with 10 wt% of cenosphere and an increase in the storage modulus up to ~30% in the composites relative to the soft PP phase. The non-essential work of fracture (NEWF: βw p) as the resistance to stable crack propagation has shown a maximum at 10 wt% of cenosphere followed by a sharp drop at higher cenosphere content indicating a cenosphere-induced ductile-to-brittle transition (DBT). Fractured surface morphology investigations revealed that the failure mode of the composites undergo a systematic transition from matrix-controlled shear deformation to filler-controlled quasi-brittle modes above a cenosphere loading of 10 wt% in the composites reiterating the possibility of filler-induced semiductile-to-DBT transition.

Influence of block composition on crack toughness behaviour of styrene- b–(styrene- random-butadiene)– b-styrene triblock copolymers

The deformation and fracture behaviour of symmetric and asymmetric styrene- b–(styrene- random-butadiene)– b-styrene (S–SB–S) triblock copolymers with variations in their molecular architectures in terms of their outer PS block and the random SB middle block composition ratios have been investigated using essential work of fracture approach based on post yield fracture mechanics concept. The present investigations on crack resistance behaviour of these S–(S/B)–S triblock copolymers where effective interaction parameter (χ eff) is systematically varied through the variation of block compositions and architecture is in continuation to our earlier communicated short article highlighting the phase behaviour-morphology and mechanical property interrelation. The crack initiation and propagation behaviours are correlated to morphology and dynamic mechanical properties as obtained from TEM, SAXS and DMA measurements. The influence of interaction parameter ( χ-parameter) space which has been manipulated through the variation of block compositions has clearly manifested in their morphologies and in their mechanical properties. Further the kinetic aspects of fracture mechanical response have also been investigated where all the materials have clearly revealed block composition dependence. SEM analysis was carried out to understand the fracture modes prior to failure.

Structural interpretations of deformation and fracture behavior of polypropylene/multi-walled carbon nanotube composites

The deformation and crack resistance behavior of polypropylene (PP) multi-walled carbon nanotube (MWNT) composites have been studied and their interrelation to the structural attributes studied by transmission electron microscopy (TEM), atomic force microscopy (AFM), scanning electron microscopy (SEM), wide-angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC) and polarization light microscopy has been discussed. The composites were produced from industrial available MWNT by extrusion melt-mixing and injection-molding. In stress–strain measurements a strong increase in the yield stress and the Young’s modulus at low MWNT contents has been observed, which was attributed to an efficient load transfer between the carbon nanotubes and polypropylene matrix through a good polymer–nanotube adhesion as indicated by SEM. The extent of enhancement in mechanical properties above 1.5 wt.% of MWNT decreased due to an apparently increased tendency of clustering of carbon nanotubes. Several theoretical models have been taken into account to explain the mechanical properties and to demonstrate the applicability of such models to the system under investigation. The crack resistance behavior has been studied with the essential work of fracture (EWF) approach based on post-yield fracture mechanics (PYFM) concept. A maximum in the non-essential work of fracture was observed at 0.5 wt.% MWNT demonstrating enhanced toughness compared to pure PP, followed by a sharp decline as the MWNT content was increased to 1.5 wt.% reveals a ductile-to-semi-ductile transition. Studies on the kinetics of crack propagation aspects have revealed a qualitative picture of the nature of such a transition in the fracture modes.

Ductile‐to‐Semiductile Transition in PP‐MWNT Nanocomposites

AbstractA ductile‐to‐semiductile transition in the crack resistance behaviour of PP/MWNT composites is discussed, using an essential work of fracture approach based on a post yield fracture mechanics concept and its possible interrelation to the structural attributes studied by TEM, SEM, and WAXD. A maximum in the non‐essential work of fracture is observed at 0.5 wt.‐% MWNT content, which demonstrates the enhanced resistance to crack propagation compared to pure PP, followed by a sharp decline with the increase in MWNT content to 1.5 wt.‐%, which reveals a ductile‐to‐semiductile transition. Fracture kinetic studies present a qualitative picture of the nature of such a transition in terms of a) switch over from non‐steady (in pure PP) to steady‐state crack tip opening displacement rate (in nanocomposites), and b) a ductile‐to‐semiductile transition; largely as a result of delayed‐yielding of the nanocomposites.magnified image

Mechanical control of a lithological alternation on normal fault morphology, growth and reactivation

Abstract This paper presents an analysis of the control of lithological variation on normal fault morphology, growth and reactivation. We study a normal fault population contained within an inter-bedded sequence of marly-limestones and clay rich layers. The analysis of cross sectional and bedding plane exposure of faults reveals that the plastic clay layers act as barriers to vertical fault propagation. Only the long vertically restricted normal faults (i.e. confined between two clay layers) are later reactivated and show extensional-shear mode of deformation. The likelihood of reactivation of the faults was probably favoured by the small plastic strength of the clay rich layers. We discuss the extensional-shear mode in terms of structural context, reactivation and rock rigidity. Displacement profile analysis of only isolated non-reactivated faults allows us to distinguish the faults mechanically influenced by the rheological discontinuities from those that are contained within the same lithological unit. Using both cross-sectional observations and displacement-length data of the fault population we estimate the average aspect ratio (length/height ~ 2) of the faults contained within the same lithological unit. A 3-D displacement-length scaling law that integrates post yield fracture mechanics (PYFM) and the principal fault dimensions (length and height) reveals the importance of the low rigidity of the marly-limestone on the displacement of the faults contained into a same lithological unit. A comparison of our displacement-length data with those compiled from the literature suggests that the displacement-length variability is strongly related to the rock mechanical properties and contrasts in layered rocks. The bulk of our analysis, based on field observations and theory, shows that: (i) fault shape, (ii) fault ability to be reactivated, (iii) shear mode, and (iv) displacement-length values are strongly sensitive to the lithological contrasts, and are therefore dependent on the fault dimension relative to the thicknesses of the sedimentary bodies. Therefore, regardless the variety of fault initiation processes, our analysis confirms that both fault morphology and fault growth are not self similar in heterogeneous layered rocks from centimetre to kilometre scale.

Effects of testing speed and heat treatment on the fracture of kaolin-reinforced high density polyethylene

In the case of ductile thermoplastic polymers in either neat form or in a composite, the volumetric fracture work is large and may be dominant, and the ideas of post-yield fracture mechanics (PYFM) are appropriate. Both surface and volumetric work depend heavily on the polymer type, morphology including crystallinity and its directionality, and reinforcement. The plastic zone often extends fully across the specimen before crack propagation proceeds, both in application and in fracture tests. An analysis appropriate to this physical behavior has been performed for polymers and has been extended to composites [1–3]. This analysis is also the subject of a proposed standard [4]. The described behavior is that of materials where fracture begins after the specimen ligament has fully yielded; that is, after the peak load has been reached. Briefly summarized, the plastic zone size can often be assumed to be proportional to the ligament length L squared with a non-dimensional proportionality constant or shape factor β which depends on the specimen geometry and material. The surface work is proportional to the surface area. The total work of fracture Wf may be normalized by the ligament surface area (LB), where B is the specimen thickness, giving

Fault tip displacement gradients and process zone dimensions

Finite displacement gradients measured at fault tips appear to contradict the predictions of the post-yield fracture mechanics (PYFM) model for fault tip propagation proposed by Cowie, P. A. and Scholz, C. H. (1992) Journal of Structural Geology, 14, 1133–1148. The results of a high resolution survey of a 3.6 km long normal fault in SE Utah are presented as evidence that the contradiction is real and not simply due to problems of limited resolution. A theoretical explanation for finite tip gradients is then proposed which involves a positive stress feedback between sequential fault slip increments. According to this growth model, strength heterogeneities on a fault surface limit the size of individual ruptures so that only a patch of the fault moves at any one time. Each slipping patch produces a stress perturbation which raises the shear stress on adjacent healed portions of the fault as well as the surrounding rock volume. Healing takes place after each slip event, allowing local strength recovery. Using a simple two-dimensional planar fault model, we show that when the size of the slipping patch is much smaller than the dimensions of the fault plane, and strength recovery is geologically instantaneous, the displacement profile follows an approximately linear decrease towards the tip similar to natural examples. A bell-shaped displacement profile, with tip gradients that tend to zero, is predicted only in the special case where the size of each slip patch equals the fault plane dimensions. Our main modification of the earlier model is that the size of the process zone wake, or frictional breakdown zone, scales with the dimensions of the slipping patch as opposed to the entire fault length. Model results show that the stress field at the tips of faults formed by this mechanism decays rapidly, so the range of significant interaction is small compared to the fault dimensions.

Fracture behaviour of long fibre reinforced thermoplastics

This paper deals with the fracture performance of injection moulded long glass fibre composites based on polybutylene terephthalate (PBT) and polypropylene (PP) matrices. The tensile behaviour of these composites is analysed using the shear lag theory taking into consideration the interfacial shear strength, fibre length distribution and fibre orientation in the mouldings. The fracture performance is investigated using the post yield fracture mechanics approach. The crack growth resistance of the PP and PBT long fibre composite was found to increase with increasing fibre volume content up to 35%. Above 35% a plateau in the fracture performance was observed. A combination of high fibre degradation and a change in the fibre orientation pattern of the moulded pieces is found to be responsible for the plateau region in the performance of the high concentration system. In fact, the dependence of the maximum crack growth resistance of the composites on fibre length and fibre orientation is also controlled by testing temperature. The competition between fibre-induced matrix deformation and the fibre pull-out determines the ability of the composites to resist crack propagation.

Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model : Cowie, P A; Scholz, C H J Struct GeolV14, N10, Nov 1992, P1133–1148

Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model : Cowie, P A; Scholz, C H J Struct GeolV14, N10, Nov 1992, P1133–1148

Physical explanation for the displacement-length relationship of faults using a post-yield fracture mechanics model

A plane strain model for a fault is presented that takes into account the inelastic deformation involved in fault growth. The model requires that the stresses at the tip of the fault never exceed the shear strength of the surrounding rock. This is achieved by taking into account a zone, around the perimeter of the fault surface, where the fault is not well developed, and in which sliding involves frictional work in excess of that required for sliding on the fully developed fault. The displacement profiles predicted by the fault model taper out gradually towards the tip of the fault and compare well with observed displacement profiles on faults. Using this model it is found that both (1) the shape of the displacement profile, and (2) the ratio of maximum displacement to fault length are a function of the shear strength of the rock in which the fault forms. For the case of a fault loaded by a constant remote stress, the displacement is linearly related to the length of the fault and the constant of proportionality depends on the shear strength of the surrounding rock normalized by its shear modulus. Using data from faults in different tectonic regions and rock types, the in situ strength of intact rock surrounding a fault is calculated to be on the order of 100 MPa (or a few kilobars). These estimates exceed, by perhaps a factor of 10, the strength of a well developed fault and thus provide an upper bound for the shear strength of the crust. It is also shown that the work required to propagate a fault scales with fault length. This result can explain the observation that the fracture energy calculated for earthquake ruptures and natural faults are several orders of magnitude greater than that for fractures in laboratory experiments.

Numerical post-yield fracture criteria comparisons on plane strain test specimens

The latest release of the BERSAFE finite element system offers several different methods for evaluating energetically-based fracture parameters for post-yield fracture mechanics. These methods all incorporate different theoretical assumptions and involve varying numerical processes which result in different degrees of accuracy in the computed quantities. Critical comparisons of the above techniques have been made on three typical plane strain test specimens. All aspects of computation are identical except for the particular evaluation of each parameter, highlighting their relative accuracies under quite high amounts of plastic yielding.

Role of morphology and coupling agent in fracture performance of glass‐filled polypropylene

AbstractThe effect of silane coupling agent on the morphology and fracture performance of particulates‐filled polypropylene was investigated. The onset of the crystallization at the filler‐matrix interface was observed by optical microscopy. This analysis shows that the silane alters the matrix morphology by inducing nucleation at the filler‐matrix interface. This effect was attributed to the physisorbed layer of silane on the filler. The fracture performance of the composites was analyzed by the post yield fracture mechanics approach. The effect of coupling agent on the fracture performance was found to occur at a very low concentration, whereas subsequent increase in silane concentration had no effect. Furthermore, the effect of coupling agent depended on concentration of filler. Silane treatment had a detrimental effect at low concentration of filler. However, at high concentration of filler, an improvement in the filler‐matrix adhesion had a beneficial effect on the fracture performance. Two phenomena, the morphological effect and the competition between the contribution of the matrix‐filler interface and the contribution of the matrix, were found to be possible explanations for the variation of KRmax with filler concentration and adhesion at the matrix‐filler interface.

Post-yield fracture mechanics analysis of the combined thermal and mechanical loading of a centre-cracked plate

The elastic-plastic stress analysis of a centre-cracked plate subjected to two types of loading is considered using the non-linear BERSAFE finite element system. The loading includes both uniaxial tension and a quadratic thermal gradient across the plate, both of which independently would tend to open the crack. In the present work the combined effect of these two load forms is investigated by applying one after the other using the restart facility. In the case of the thermal load followed by the tensile load, several restarts of the tensile part were made at successively lower thermal loads. Also, both combinations of load application were applied to a plate initially uncracked, then the crack was opened from the loaded state by using a nodal load release technique. In all cases, path independent contour integrals were calculated to assess the fracture conditions at the crack tip under the above styles of loading, particularly with a view to supplying results which can be compared to proposed CEGB fracture procedures.

Statistical evaluation of post-yield fracture mechanics properties on the basis of the notched bar impact test

Abstract By means of the test results it could be shown that a correlation exists between the ductile fracture mechanics parameters for crack initiation J i and J Ic and the notch impact energy, in which initially only values from the upper shelf of the notch energy were taken into consideration. Owing to a statistical evaluation and with the aid of the relationships indicated, the user can chose the probability with which the value selected is to be situated within the range in question by which the width of the scatter is presupposed. By consideration of all the distributed values, specifically the J i , J Ic and J 50 impact energy values and the material characteristic values from the tensile test, it could be demonstrated on two vessels made of modified 22 NiMoCr 3 7 (60 J on the upper shelf of the notch impact energy) and 20 MnMoNi 5 5 (200 J on the upper shelf of the notch impact energy) respectively with axial external cracks that the experimental instability load can be assigned to the upper bound of the scatter band formed from the crack initiation values J i ( J Ic ).

Transferability of post yield fracture mechanics properties from small scale specimens to large scale specimens and components

This contribution describes a method for the determination of the J-integral as a function of the load-line displacement for arbitrary specimen geometries. A correspondence could be found between the approximation method and the results determining with the Rice integral by means of a FE-calculation. Using the initiation values of the J-integral as a fracture mechanics parameter determined from the J R-curve, correspond with failure values of double-édged notched tensile specimens and circumferentially notched round tensile specimens of which crack initiation was tantamount to instability. Consequently, it could be proved that the J-integral is a transferable parameter that may be ascertained from simple determinable deformation values. The application to real components seems to be promising, due to these good results.

Numerical simulation of post yield fracture mechanics experiments as a basis for the transferability to components

As a necessary step in the chain of transferability from small specimens to actual structures the numerical evaluations of two crack-growth resistance experiments on the basis of the J-integral and utilising sidegrooved compact specimens of different sizes, tested at room temperature and at 285°C are discussed. The necessary experimental and numerical techniques are presented: • -The partial unloading technique as applied in the IWM is applicable with high accuracy and reproducability in the relevant temperature range up to operating temperature. • -The J-evaluation combined with a node shifting and releasing technique as implemented in the IWM-version of ADINA proved to be a powerful and economic tool even for parameter studies. The results of the experiments and of the numerical evaluations are presented as force-displacement diagrams and as J-integral vs. crack extension curves. The good qualitative and quantitative agreement supports the experimental evaluation of J from the force-displacement diagram and validitates the numerical procedures to be applied and extended to real structues.

A comparison of theJ* integral with other methods of post yield fracture mechanics

TheJ* integral approach to post yield fracture analysis is compared with a wide variety of other methods by means of experimental testing of specimens invalid in the sense of ASTM. The significance of J* and its relationship to other integrals is discussed.